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physics

mechanics

Easy

Question

$space A space u n i f o r m space r o d space s m o o t h l y space p i v o t e d space a t space o n e space o f space i t s space e n d s space i s space r e l e a s e d space f r o m space r e s t. space I f space i t space s w i n g s space i n space v e r t i c a l space p l a n e comma space t h e space m a x i m u m space s p e e d space o f space t h e space e n d space P space o f space t h e space r o d space i s$

$2 \sqrt{3 g l}$
$\sqrt{3 g l}$
$2 \sqrt{2 g l}$
$\sqrt{g l}$

The correct answer is: $\sqrt{3 g l}$

$A t space t h e space t i m e space o f space m a x i m u m space s p e e d space o f space p o i n t space P comma space t h e space r o d space s h o u l d space b e space v e r t i c a l table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell straight capital delta K plus straight capital delta U equals 0 end cell row cell open square brackets 1 half open parentheses fraction numerator m ell squared over denominator 3 end fraction close parentheses omega squared minus 0 close square brackets plus open square brackets negative m g ell over 2 close square brackets equals 0 not stretchy rightwards double arrow omega equals square root of fraction numerator 3 g over denominator ell end fraction end root end cell end table text Velocity of point end text P V subscript P equals omega ell equals square root of 3 g ell end root$

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